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金融民工阿聪 · 2020年07月12日

问一道题:NO.PZ2016070201000067

问题如下:

Using Model 2, assume a current short-term rate of 8%, an annual drift of 50bps, and a short-term rate standard deviation of 2%. In addition, assume the ex-post realization of the dw random variable is 0.3. After constructing a 2-period interest rate tree with annual periods, what is the interest rate in the middle node at the end of year 2?

选项:

A.

8.0%.

B.

8.8%.

C.

9.0%.

D.

9.6%.

解释:

Using Model 2 notation:

current short-term rate, r0  = 8% drift, λ = 0.5% standard deviation, σ = 2% random variable, dw = 0.3 change in time, dt =1

Since we are asked to find the interest rate at the second period middle node using Model 2, we know the tree will recombine to the following rate: r0 + 2 λ.dt.

8% + 2 x 0.5% x 1 = 9%

这里为什么dt不能是2,不是说两年吗,我看有类似的提问,但是无法解决我的疑问。

他不是说了construct a 2-period interest rate tree with annual periods吗,用年度的概念去构建一个2-period的利率二叉树,那不就是2个年度构建成一个2-period的二叉树吗,那dt不就是2了吗?

1 个答案

袁园_品职助教 · 2020年07月12日

同学你好!

dt针对的是一期,本题中一期是一年